Method of Increments Valence-band Structure and Bandgap

3 Method of Increments Valence-band Structure and Bandgap 

The incremental scheme based on the wavefunction HF method was extended to the calculation of valence-band energies when the electron-correlation is taken into account. In [176,177] an effective Hamiltonian for the N — l)-electron system was set up in terms of local matrix elements derived from multireference configuration-interaction (MRCI) calcnlations for finite clnsters. This allowed correlation corrections to a HF band strnctnre to be expressed and rehable results obtained for the valence-band structure of covalent semicondnctors. A related method based on an efiective Hamiltonian in locahzed Wannier-type orbitals has also been proposed and applied to polymers [178,179]. Later, the incremental scheme was used to estimate the relative energies of valence-band states and also yield absolnte positions of snch states [180]. 

This is important as a prerequisite for the determination of bandgaps. Unfortunately, a further extension of the formalism to also cover conduction-band states (which would complete the information on bandgaps) is not possible along the same Unes. 

The incremental scheme for the valence band rests on the observation that a HF-hole can be either described in reciprocal or in direct space. In reciprocal space, the (A -l)-electron states are introduced 

The states ki/) can be approximated in terms of basis functions adapted to trans- 

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